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<h1><img src="../../../../boost.png" alt="boost.png (6897 bytes)" align=
"middle" width="277" height="86">Boost.MultiIndex Tutorial: Basics</h1>

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<h2>Contents</h2>

<ul>
  <li><a href="#intro">Introduction</a>
    <ul>
      <li><a href="#multiple_sort">Multiple sorts on a single set</a></li>
      <li><a href="#list_fast_lookup">A bidirectional list with fast lookup</a></li>
    </ul>
  </li>
  <li><a href="#index_spec">Index specification</a></li>
  <li><a href="#tagging">Tagging</a></li>
  <li><a href="#iterator_access">Iterator access</a></li>
  <li><a href="#index_types">Index types</a>
    <ul>
      <li><a href="#ord_indices">Ordered indices</a>
        <ul>
          <li><a href="#unique_non_unique">Unique and non-unique variants</a></li>
          <li><a href="#ord_spec">Specification</a></li>
          <li><a href="#key_extraction">Key extraction</a></li>
          <li><a href="#comparison_predicates">Comparison predicates</a></li>
          <li><a href="#special_lookup">Special lookup operations</a></li>
          <li><a href="#range">Retrieval of ranges</a></li>
          <li><a href="#ord_updating">Updating</a></li>
        </ul>
      </li>
      <li><a href="#seq_indices">Sequenced indices</a>
        <ul>
          <li><a href="#seq_spec">Specification</a></li>
          <li><a href="#list_ops">List operations</a></li>
          <li><a href="#seq_updating">Updating</a></li>
        </ul>
      </li>
    </ul>
  </li>
  <li><a href="#projection">Projection of iterators</a></li>
  <li><a href="#complexity">Complexity and exception safety</a></li>
</ul>

<h2><a name="intro">Introduction</a></h2>

<p>
We introduce the main concepts of Boost.MultiIndex through the study of
two typical use cases.
</p>

<h3><a name="multiple_sort">Multiple sorts on a single set</a></h3>

<p>
STL sets and multisets are varying-length containers where elements are efficiently
sorted according to a given comparison predicate. These container classes fall short
of functionality when the programmer wishes to efficiently sort and look up the elements
following a different sorting criterion. Consider for instance:
</p>

<blockquote><pre>
<span class=keyword>struct</span> <span class=identifier>employee</span>
<span class=special>{</span>
  <span class=keyword>int</span>         <span class=identifier>id</span><span class=special>;</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span> <span class=identifier>name</span><span class=special>;</span>

  <span class=identifier>employee</span><span class=special>(</span><span class=keyword>int</span> <span class=identifier>id</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>name</span><span class=special>):</span><span class=identifier>id</span><span class=special>(</span><span class=identifier>id</span><span class=special>),</span><span class=identifier>name</span><span class=special>(</span><span class=identifier>name</span><span class=special>){}</span>

  <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>&lt;(</span><span class=keyword>const</span> <span class=identifier>employee</span><span class=special>&amp;</span> <span class=identifier>e</span><span class=special>)</span><span class=keyword>const</span><span class=special>{</span><span class=keyword>return</span> <span class=identifier>id</span><span class=special>&lt;</span><span class=identifier>e</span><span class=special>.</span><span class=identifier>id</span><span class=special>;}</span>
<span class=special>};</span>
</pre></blockquote>

<p>The fact that IDs are unique to each employee is reflected by the way
<code>operator&lt;</code> is defined, so a natural data structure for storing of
<code>employee</code>s is just a <code>std::set&lt;employee></code>. Now,
if one wishes to print out a listing of all employees in alphabetical order, available
solutions may have disadvantages either in terms of storage space, complexity or ease
of maintenance:
<ul>
<li>Copy the employee set into a vector or similar and sort this by a comparison
functor dependent upon <code>employee::name</code>.
<li>Keep a secondary data structure of pointers to the elements of the set, appropriately
sorted by name.
</ul>
Of these, probably the second solution will be the one adopted by most programmers
concerned about efficiency, but it imposes the annoying burden of keeping the two
structures in sync. If the code is additionally required to be exception-safe, this
construct easily becomes unmaintainable.
</p>

<p>
Boost.MultiIndex features <a href="#ord_indices"><i>ordered indices</i></a>, which
sort the elements according to a particular key, and are designed to help programmers
in need of sequences of elements for which <i>more than one</i> sorting criteria are
relevant. We do so by defining a <code>multi_index_container</code>
instantiation composed of several ordered indices: each index, viewed in isolation,
behaves much as an ordered <code>std::set</code> (or <code>std::multiset</code>), whilst
the overall integrity of the entire data structure is preserved. Our example problem
thus can be solved with Boost.MultiIndex as follows:
</p>

<blockquote><pre>
<span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>boost</span><span class=special>/</span><span class=identifier>multi_index_container</span><span class=special>.</span><span class=identifier>hpp</span><span class=special>&gt;</span>
<span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>boost</span><span class=special>/</span><span class=identifier>multi_index</span><span class=special>/</span><span class=identifier>ordered_index</span><span class=special>.</span><span class=identifier>hpp</span><span class=special>&gt;</span>
<span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>boost</span><span class=special>/</span><span class=identifier>multi_index</span><span class=special>/</span><span class=identifier>identity</span><span class=special>.</span><span class=identifier>hpp</span><span class=special>&gt;</span>
<span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>boost</span><span class=special>/</span><span class=identifier>multi_index</span><span class=special>/</span><span class=identifier>member</span><span class=special>.</span><span class=identifier>hpp</span><span class=special>&gt;</span>

<span class=comment>// define a multiply indexed set with indices by id and name</span>
<span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span>
  <span class=identifier>employee</span><span class=special>,</span>
  <span class=identifier>indexed_by</span><span class=special>&lt;</span>
    <span class=comment>// sort by employee::operator&lt;</span>
    <span class=identifier>ordered_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>&gt;</span> <span class=special>&gt;,</span>
    
    <span class=comment>// sort by less&lt;string&gt; on name</span>
    <span class=identifier>ordered_non_unique</span><span class=special>&lt;</span><span class=identifier>member</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>,</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>,&amp;</span><span class=identifier>employee</span><span class=special>::</span><span class=identifier>name</span><span class=special>&gt;</span> <span class=special>&gt;</span>
  <span class=special>&gt;</span> 
<span class=special>&gt;</span> <span class=identifier>employee_set</span><span class=special>;</span>

<span class=keyword>void</span> <span class=identifier>print_out_by_name</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>employee_set</span><span class=special>&amp;</span> <span class=identifier>es</span><span class=special>)</span>
<span class=special>{</span>
  <span class=comment>// get a view to index #1 (name)</span>
  <span class=keyword>const</span> <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>nth_index</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;::</span><span class=identifier>type</span><span class=special>&amp;</span> <span class=identifier>name_index</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;();</span>
  <span class=comment>// use name_index as a regular std::set</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>copy</span><span class=special>(</span>
    <span class=identifier>name_index</span><span class=special>.</span><span class=identifier>begin</span><span class=special>(),</span><span class=identifier>name_index</span><span class=special>.</span><span class=identifier>end</span><span class=special>(),</span>
    <span class=identifier>std</span><span class=special>::</span><span class=identifier>ostream_iterator</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>&gt;(</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>cout</span><span class=special>));</span>
<span class=special>}</span>
</pre></blockquote>

<p>
Instead of a single comparison predicate type, as it happens for STL associative
containers, <code>multi_index_container</code> is passed a 
<a href="../reference/multi_index_container.html#multi_index_container">list</a> of index
specifications (<code>indexed_by</code>), each one inducing the corresponding index.
Indices are accessed via
<a href="../reference/multi_index_container.html#index_retrieval"><code>get</code></a><code>&lt;N>()</code>
where <i>N</i> ranges between 0 and the number of comparison
predicates minus one. The functionality of index #0 can be accessed directly from a
<code>multi_index_container</code> object without using <code>get&lt;0>()</code>: for instance,
<code>es.begin()</code> is equivalent to <code>es.get&lt;0>().begin()</code>.
</p>

<p>
Note that <code>get</code> returns a <i>reference</i> to the index, and not
an index object. Indices cannot be constructed as separate objects from the
container they belong to, so the following
</p>

<blockquote><pre>
<span class=comment>// Wrong: we forgot the &amp; after employee_set::nth_index&lt;1&gt;::type</span>
<span class=keyword>const</span> <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>nth_index</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>name_index</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;();</span>
</pre></blockquote>

<p>
does not compile, since it is trying to construct the index object
<code>name_index</code>. This is a common source of errors in user code.
</p>

<h3><a name="list_fast_lookup">A bidirectional list with fast lookup</a></h3>

<p>
This study case allows us to introduce so-called
<a href="#seq_indices"><i>sequenced indices</i></a>, and how they
interact with ordered indices to construct powerful containers. Suppose
we have a text parsed into words and stored in a list like this:
</p>

<blockquote><pre>
<span class=keyword>typedef</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>list</span><span class=special>&lt;</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&gt;</span> <span class=identifier>text_container</span><span class=special>;</span>

<span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span> <span class=identifier>text</span><span class=special>=</span>
  <span class=string>&quot;Alice was beginning to get very tired of sitting by her sister on the &quot;</span>
  <span class=string>&quot;bank, and of having nothing to do: once or twice she had peeped into the &quot;</span>
  <span class=string>&quot;book her sister was reading, but it had no pictures or conversations in &quot;</span>
  <span class=string>&quot;it, 'and what is the use of a book,' thought Alice 'without pictures or &quot;</span>
  <span class=string>&quot;conversation?'&quot;</span><span class=special>;</span>

<span class=comment>// feed the text into the list</span>
<span class=identifier>text_container</span> <span class=identifier>tc</span><span class=special>;</span>
<span class=identifier>boost</span><span class=special>::</span><span class=identifier>tokenizer</span><span class=special>&lt;</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>char_separator</span><span class=special>&lt;</span><span class=keyword>char</span><span class=special>&gt;</span> <span class=special>&gt;</span> <span class=identifier>tok</span>
  <span class=special>(</span><span class=identifier>text</span><span class=special>,</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>char_separator</span><span class=special>&lt;</span><span class=keyword>char</span><span class=special>&gt;(</span><span class=string>&quot; \t\n.,;:!?'\&quot;-&quot;</span><span class=special>));</span>
<span class=identifier>std</span><span class=special>::</span><span class=identifier>copy</span><span class=special>(</span><span class=identifier>tok</span><span class=special>.</span><span class=identifier>begin</span><span class=special>(),</span><span class=identifier>tok</span><span class=special>.</span><span class=identifier>end</span><span class=special>(),</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>back_inserter</span><span class=special>(</span><span class=identifier>tc</span><span class=special>));</span>
</pre></blockquote>

<p>
If we want to count the occurrences of a given word into the text we will resort
to <code>std::count</code>:
</p>

<blockquote><pre>
<span class=identifier>std</span><span class=special>::</span><span class=identifier>size_t</span> <span class=identifier>occurrences</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>word</span><span class=special>)</span>
<span class=special>{</span>
  <span class=keyword>return</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>count</span><span class=special>(</span><span class=identifier>tc</span><span class=special>.</span><span class=identifier>begin</span><span class=special>(),</span><span class=identifier>tc</span><span class=special>.</span><span class=identifier>end</span><span class=special>(),</span><span class=identifier>word</span><span class=special>);</span>
<span class=special>}</span>
</pre></blockquote>

<p>
But this implementation of <code>occurrences</code> performs in linear time, which
could be unacceptable for large quantities of text. Similarly, other operations like
deletion of selected words are just too costly to carry out on a
<code>std::list</code>:
</p>

<blockquote><pre>
<span class=keyword>void</span> <span class=identifier>delete_word</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>word</span><span class=special>)</span>
<span class=special>{</span>
  <span class=identifier>tc</span><span class=special>.</span><span class=identifier>remove</span><span class=special>(</span><span class=identifier>word</span><span class=special>);</span> <span class=comment>// scans the entire list looking for word</span>
<span class=special>}</span>
</pre></blockquote>

<p>
When performance is a concern, we will need an additional data structure that indexes
the elements in <code>tc</code>, presumably in alphabetical order. Boost.MultiIndex
does precisely this through the combination of sequenced and ordered indices:
</p>

<blockquote><pre>
<span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>boost</span><span class=special>/</span><span class=identifier>multi_index_container</span><span class=special>.</span><span class=identifier>hpp</span><span class=special>&gt;</span>
<span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>boost</span><span class=special>/</span><span class=identifier>multi_index</span><span class=special>/</span><span class=identifier>sequenced_index</span><span class=special>.</span><span class=identifier>hpp</span><span class=special>&gt;</span>
<span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>boost</span><span class=special>/</span><span class=identifier>multi_index</span><span class=special>/</span><span class=identifier>ordered_index</span><span class=special>.</span><span class=identifier>hpp</span><span class=special>&gt;</span>
<span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>boost</span><span class=special>/</span><span class=identifier>multi_index</span><span class=special>/</span><span class=identifier>identity</span><span class=special>.</span><span class=identifier>hpp</span><span class=special>&gt;</span>

<span class=comment>// define a multi_index_container with a list-like index and an ordered index</span>
<span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>,</span>
  <span class=identifier>indexed_by</span><span class=special>&lt;</span>
    <span class=identifier>sequenced</span><span class=special>&lt;&gt;,</span> <span class=comment>// list-like index</span>
    <span class=identifier>ordered_non_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&gt;</span> <span class=special>&gt;</span> <span class=comment>// words by alphabetical order</span>
  <span class=special>&gt;</span>
<span class=special>&gt;</span> <span class=identifier>text_container</span><span class=special>;</span>

<span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span> <span class=identifier>text</span><span class=special>=...</span>

<span class=comment>// feed the text into the list</span>
<span class=identifier>text_container</span> <span class=identifier>tc</span><span class=special>;</span>
<span class=identifier>boost</span><span class=special>::</span><span class=identifier>tokenizer</span><span class=special>&lt;</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>char_separator</span><span class=special>&lt;</span><span class=keyword>char</span><span class=special>&gt;</span> <span class=special>&gt;</span> <span class=identifier>tok</span>
  <span class=special>(</span><span class=identifier>text</span><span class=special>,</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>char_separator</span><span class=special>&lt;</span><span class=keyword>char</span><span class=special>&gt;(</span><span class=string>&quot; \t\n.,;:!?'\&quot;-&quot;</span><span class=special>));</span>
<span class=identifier>std</span><span class=special>::</span><span class=identifier>copy</span><span class=special>(</span><span class=identifier>tok</span><span class=special>.</span><span class=identifier>begin</span><span class=special>(),</span><span class=identifier>tok</span><span class=special>.</span><span class=identifier>end</span><span class=special>(),</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>back_inserter</span><span class=special>(</span><span class=identifier>tc</span><span class=special>));</span>
</pre></blockquote>

<p>
So far, the substitution of <code>multi_index_container</code> for <code>std::list</code>
does not show any advantage. The code for inserting the text into the container
does not change as sequenced indices provide an interface similar to that of
<code>std::list</code> (no explicit access to this index through
<code>get&lt;0>()</code> is needed as <code>multi_index_container</code> inherits the
functionality of index #0.) But the specification of an additional ordered index
allows us to implement <code>occurrences</code> and <code>delete_word</code>
in a much more efficient manner:
</p>

<blockquote><pre>
<span class=identifier>std</span><span class=special>::</span><span class=identifier>size_t</span> <span class=identifier>occurrences</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>word</span><span class=special>)</span>
<span class=special>{</span>
  <span class=comment>// get a view to index #1</span>
  <span class=identifier>text_container</span><span class=special>::</span><span class=identifier>nth_index</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;::</span><span class=identifier>type</span><span class=special>&amp;</span> <span class=identifier>sorted_index</span><span class=special>=</span><span class=identifier>tc</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;();</span>

  <span class=comment>// use sorted_index as a regular std::set</span>
  <span class=keyword>return</span> <span class=identifier>sorted_index</span><span class=special>.</span><span class=identifier>count</span><span class=special>(</span><span class=identifier>word</span><span class=special>);</span>
<span class=special>}</span>

<span class=keyword>void</span> <span class=identifier>delete_word</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>word</span><span class=special>)</span>
<span class=special>{</span>
  <span class=comment>// get a view to index #1</span>
  <span class=identifier>text_container</span><span class=special>::</span><span class=identifier>nth_index</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;::</span><span class=identifier>type</span><span class=special>&amp;</span> <span class=identifier>sorted_index</span><span class=special>=</span><span class=identifier>tc</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;();</span>

  <span class=comment>// use sorted_index as a regular std::set</span>
  <span class=identifier>sorted_index</span><span class=special>.</span><span class=identifier>erase</span><span class=special>(</span><span class=identifier>word</span><span class=special>);</span>
<span class=special>}</span>
</pre></blockquote>

<p>
Now, <code>occurrences</code> and <code>delete_word</code> have logarithmic
complexity. The programmer can use index #0 for accessing the text as with
<code>std::list</code>, and use index #1 when logarithmic lookup is needed.
</p>

<h2>
<a name="index_spec">Index specification</a>
</h2>

<p>
The indices of a <code>multi_index_container</code> instantiation are specified by
means of the <a href="../reference/indices.html#indexed_by">
<code>indexed_by</code></a> construct. For instance, the instantiation
</p>

<blockquote><pre>
<span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span>
  <span class=identifier>employee</span><span class=special>,</span>
  <span class=identifier>indexed_by</span><span class=special>&lt;</span>
    <span class=identifier>ordered_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>&gt;</span> <span class=special>&gt;,</span>
    <span class=identifier>ordered_non_unique</span><span class=special>&lt;</span><span class=identifier>member</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>,</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>,&amp;</span><span class=identifier>employee</span><span class=special>::</span><span class=identifier>name</span><span class=special>&gt;</span> <span class=special>&gt;</span>
  <span class=special>&gt;</span> 
<span class=special>&gt;</span> <span class=identifier>employee_set</span><span class=special>;</span>
</pre></blockquote>

<p>
is comprised of a <a href="#unique_non_unique">unique ordered index</a> and a
<a href="#unique_non_unique">non-unique ordered index</a>, while in
</p>

<blockquote><pre>
<span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>,</span>
  <span class=identifier>indexed_by</span><span class=special>&lt;</span>
    <span class=identifier>sequenced</span><span class=special>&lt;&gt;,</span>
    <span class=identifier>ordered_non_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&gt;</span> <span class=special>&gt;</span>
  <span class=special>&gt;</span>
<span class=special>&gt;</span> <span class=identifier>text_container</span><span class=special>;</span>
</pre></blockquote>

<p>
we specifiy two indices, the first of <a href="#seq_indices">sequenced type</a>,
the second a non-unique <a href="#ord_indices">ordered index</a>. In general, we
can specify an arbitrary number of indices: each of the arguments of
<code>indexed_by</code> is called an
<a href="../reference/indices.html#index_specification"><i>index specifier</i></a>.
Depending on the type of index being specified, the corresponding specifier
will need additional information: for instance, the specifiers <code>ordered_unique</code>
and <code>ordered_non_unique</code> are provided with a
<a href="#key_extraction">key extractor</a> and an optional
<a href="#comparison_predicates">comparison predicate</a> which jointly indicate
how the sorting of elements will be performed.
</p>

<p>
A <code>multi_index_container</code> instantiation can be declared without supplying
the <code>indexed_by</code> part: in this case, default index values are taken
so that the resulting type is equivalent to a regular <code>std::set</code>.
Concretely, the instantiation
</p>

<blockquote><pre>
<span class=identifier>multi_index_container</span><span class=special>&lt;</span><i>(element)</i><span class=special>&gt;</span>
</pre></blockquote>

<p>
is equivalent to
</p>

<blockquote><pre>
<span class=identifier>multi_index_container</span><span class=special>&lt;</span>
  <i>(element)</i><span class=special>,</span>
  <span class=identifier>indexed_by</span><span class=special>&lt;</span>
    <span class=identifier>ordered_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;(</span><span class=identifier>element</span><span class=special>)&gt;</span> <span class=special>&gt;</span>
  <span class=special>&gt;</span>
<span class=special>&gt;</span>
</pre></blockquote>

<h2><a name="tagging">Tagging</a></h2>

<p>
In order to retrieve (a reference to) an index of a given <code>multi_index_container</code>,
the programmer must provide its order number, which is cumbersome and not very
self-descriptive. Optionally, indices can be assigned <i>tags</i> (C++ types) that
act as more convenient mnemonics. If provided, tags must be passed as the
first parameter of the corresponding index specifier. The following is a revised version of
<code>employee_set</code> with inclusion of tags:
</p>

<blockquote><pre>
<span class=comment>// tags</span> 
<span class=keyword>struct</span> <span class=identifier>name</span><span class=special>{};</span>

<span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span>
  <span class=identifier>employee</span><span class=special>,</span>
  <span class=identifier>indexed_by</span><span class=special>&lt;</span>
    <span class=identifier>ordered_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>&gt;</span> <span class=special>&gt;,</span>
    <span class=identifier>ordered_non_unique</span><span class=special>&lt;</span><span class=identifier>tag</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;,</span><span class=identifier>member</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>,</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>,&amp;</span><span class=identifier>employee</span><span class=special>::</span><span class=identifier>name</span><span class=special>&gt;</span> <span class=special>&gt;</span>
  <span class=special>&gt;</span>
<span class=special>&gt;</span> <span class=identifier>employee_set</span><span class=special>;</span>
</pre></blockquote>

<p>
Tags have to be passed inside the <a href="../reference/indices.html#tag"><code>tag</code></a>
construct. Any type can be used as a tag for an index, although in general one will choose
names that are descriptive of the index they are associated with. The tagging mechanism allows
us to write expressions like</p>

<blockquote><pre>
<span class=keyword>typedef</span> <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>index</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>employee_set_by_name</span><span class=special>;</span>
<span class=identifier>employee_set_by_name</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;().</span><span class=identifier>begin</span><span class=special>();</span>
</pre></blockquote>

<p>
If no tag is provided for an index (as is the case for index #0 of the previous
example), access to that index can only be performed by number. Note the existence
of two different <code>typedef</code>s <code>nth_index</code> and
<code>index</code> for referring to an index by number and by tag, respectively;
for instance,
<ul>
  <li><code>employee_set::nth_index&lt;1>::type</code> is the type of
    index #1,</li>
  <li><code>employee_set::index&lt;name>::type</code> is the type of the index
    tagged with <code>name</code> (the same index #1 in this case.)</li>
</ul>
<code>get()</code>, on the other hand, is overloaded to serve both styles of access:
</p>

<blockquote><pre>
<span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>index</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;::</span><span class=identifier>type</span><span class=special>&amp;</span> <span class=identifier>name_index</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;();</span>
<span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>nth_index</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;::</span><span class=identifier>type</span><span class=special>&amp;</span> <span class=identifier>name_index2</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;();</span> <span class=comment>// same index</span>
</pre></blockquote>

<p>
Additionally, the <code>tag</code> class template accepts several tags for one
index, that we can use interchangeably: for instance, the specification of index #1
in the previous example can be rewritten to hold two different tags
<code>name</code> and <code>by_name</code>:
</p>

<blockquote><pre>
<span class=comment>// tags</span>
<span class=keyword>struct</span> <span class=identifier>name</span><span class=special>{};</span>
<span class=keyword>struct</span> <span class=identifier>by_name</span><span class=special>{};</span>

<span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span>
  <span class=special>...</span>
    <span class=identifier>ordered_non_unique</span><span class=special>&lt;</span>
      <span class=identifier>tag</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>,</span><span class=identifier>by_name</span><span class=special>&gt;,</span>
      <span class=identifier>member</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>,</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>,&amp;</span><span class=identifier>employee</span><span class=special>::</span><span class=identifier>name</span><span class=special>&gt;</span>
    <span class=special>&gt;</span>
  <span class=special>...</span>
<span class=special>&gt;</span> <span class=identifier>employee_set</span><span class=special>;</span>
</pre></blockquote>

<h2><a name="iterator_access">Iterator access</a></h2>

<p>
Each index of a <code>multi_index_container</code> uses its own
iterator types, which are different from those of another indices. As is
the rule with STL containers, these iterators are defined as nested
types of the index:
</p>

<blockquote><pre>
<span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>nth_index</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;::</span><span class=identifier>type</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it</span><span class=special>=</span>
  <span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;().</span><span class=identifier>find</span><span class=special>(</span><span class=string>&quot;Judy Smith&quot;</span><span class=special>);</span>
</pre></blockquote>

<p>
This kind of expressions can be rendered more readable by
means of user-defined <code>typedef</code>s:
</p>

<blockquote><pre>
<span class=keyword>typedef</span> <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>nth_index</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>employee_set_by_name</span><span class=special>;</span>
<span class=identifier>employee_set_by_name</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it</span><span class=special>=</span>
  <span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;().</span><span class=identifier>find</span><span class=special>(</span><span class=string>&quot;Judy Smith&quot;</span><span class=special>);</span>
</pre></blockquote>

<p>
The iterators provided by every index are <i>constant</i>, that is, the elements they point to
cannot be mutated directly. This  follows the interface of <code>std::set</code> for ordered
indices but might come as a surprise for other types such as sequenced indices, which are modeled after
<code>std::list</code>, where this limitation does not happen. This seemingly odd behavior
is imposed by the way <code>multi_index_container</code>s work; if elements were
allowed to be mutated indiscriminately, we could introduce inconsistencies
in the ordered indices of the <code>multi_index_container</code> without the container
being notified about it. Element modification is properly done by means of
<a href="#ord_updating">update operations</a> on any index.
</p>

<h2>
<a name="index_types">Index types</a>
</h2>

<p>
Currently, Boost.MultiIndex provides the following index types:
<ul>
  <li>Ordered indices sort the elements like <code>std::set</code>s do and
    provide a similar interface. There are <i>unique</i> and <i>non-unique</i>
    variants: the former do not allow for duplicates, while the latter permit
    them (like <code>std::multiset</code>.)</li>
  <li>Ranked indices are a variation of ordered indices providing extra capabilities
    for querying and accessing elements based on their <i>rank</i> (the numerical position
    they occupy in the index).
  </li>
  <li>Sequenced indices are modeled after the semantics and interface of
    <code>std::list</code>: they arrange the elements as if in a bidirectional
    list.</li>
  <li>Hashed indices provide fast access to the elements through hashing
    techniques, in a similar way as unordered associative containers
    <code>std::unordered_set</code> (if duplicates are not allowed) and
    <code>std::unordered_multiset</code> (if they are).</li>
  <li>Random access indices provide an interface similar to that of
    sequenced indices, and additionally feature random access iterators
    and positional access to the elements.</li>
</ul>
The examples in the <a href="#intro">introduction</a> exercise ordered and sequenced
indices, which are the most commonly used; the other kinds of indices are presented
in the <a href="indices.html">index types</a> section of the tutorial.
</p>

<h3>
<a name="ord_indices">Ordered indices</a>
</h3>

<p>
Ordered indices sort the elements in a <code>multi_index_container</code> according
to a specified key and an associated comparison predicate. These indices can
be viewed as analogues of the standard container <code>std::set</code>, and in fact
they do replicate its interface, albeit with some minor differences dictated
by the general constraints of Boost.MultiIndex.
</p>

<h4>
<a name="unique_non_unique">Unique and non-unique variants</a>
</h4>

<p>
Ordered indices are classified into <i>unique</i>, which prohibit two
elements to have the same key value, and <i>non-unique</i> indices,
which allow for duplicates. Consider again the definition
</p>

<blockquote><pre>
<span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span>
  <span class=identifier>employee</span><span class=special>,</span>
  <span class=identifier>indexed_by</span><span class=special>&lt;</span>
    <span class=identifier>ordered_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>&gt;</span> <span class=special>&gt;,</span>
    <span class=identifier>ordered_non_unique</span><span class=special>&lt;</span><span class=identifier>member</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>,</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>,&amp;</span><span class=identifier>employee</span><span class=special>::</span><span class=identifier>name</span><span class=special>&gt;</span> <span class=special>&gt;</span>
  <span class=special>&gt;</span> 
<span class=special>&gt;</span> <span class=identifier>employee_set</span><span class=special>;</span>
</pre></blockquote>

<p>
In this instantiation of <code>multi_index_container</code>, the first index is to be
treated as unique (since IDs are exclusive to each employee) and thus is declared using
<code>ordered_unique</code>, whereas the second index is non-unique (as the possibility exists
that say two John Smiths are hired in the same company), which is specified by the use
of <code>ordered_non_unique</code>.
</p>

<p>
The classification of ordered indices in unique and non-unique has an impact on which
elements are allowed to be inserted into a given <code>multi_index_container</code>; briefly put,
unique ordered indices mimic the behavior of <code>std::set</code>s while non-unique
ordered indices are similar to <code>std::multiset</code>s. For instance, an
<code>employee_set</code> can hold the objects <code>employee(0,"George Brown")</code>
and <code>employee(1,"George Brown")</code>, but will not accept the insertion of an
<code>employee</code> object whose ID coincides with that of some previously inserted
employee.
</p>

<p>
More than one unique index can be specified. For instance, if we augment
<code>employee</code> to include an additional member for the Social Security number,
which is reasonably treated as unique, the following captures this design:
</p>

<blockquote><pre>
<span class=keyword>struct</span> <span class=identifier>employee</span>
<span class=special>{</span>
  <span class=keyword>int</span>         <span class=identifier>id</span><span class=special>;</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span> <span class=identifier>name</span><span class=special>;</span>
  <span class=keyword>int</span>         <span class=identifier>ssnumber</span><span class=special>;</span>

  <span class=identifier>employee</span><span class=special>(</span><span class=keyword>int</span> <span class=identifier>id</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>name</span><span class=special>,</span><span class=keyword>int</span> <span class=identifier>ssnumber</span><span class=special>):</span>
    <span class=identifier>id</span><span class=special>(</span><span class=identifier>id</span><span class=special>),</span><span class=identifier>name</span><span class=special>(</span><span class=identifier>name</span><span class=special>),</span><span class=identifier>ssnumber</span><span class=special>(</span><span class=identifier>ssnumber</span><span class=special>){}</span>

  <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>&lt;(</span><span class=keyword>const</span> <span class=identifier>employee</span><span class=special>&amp;</span> <span class=identifier>e</span><span class=special>)</span><span class=keyword>const</span><span class=special>{</span><span class=keyword>return</span> <span class=identifier>id</span><span class=special>&lt;</span><span class=identifier>e</span><span class=special>.</span><span class=identifier>id</span><span class=special>;}</span>
<span class=special>};</span>

<span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span>
  <span class=identifier>employee</span><span class=special>,</span>
  <span class=identifier>indexed_by</span><span class=special>&lt;</span>
    <span class=comment>// sort by employee::operator&lt;</span>
    <span class=identifier>ordered_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>&gt;</span> <span class=special>&gt;,</span>
    
    <span class=comment>// sort by less&lt;string&gt; on name</span>
    <span class=identifier>ordered_non_unique</span><span class=special>&lt;</span><span class=identifier>member</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>,</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>,&amp;</span><span class=identifier>employee</span><span class=special>::</span><span class=identifier>name</span><span class=special>&gt;</span> <span class=special>&gt;,</span>
    
    <span class=comment>// sort by less&lt;int&gt; on ssnumber</span>
    <span class=identifier>ordered_unique</span><span class=special>&lt;</span><span class=identifier>member</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>,</span><span class=keyword>int</span><span class=special>,&amp;</span><span class=identifier>employee</span><span class=special>::</span><span class=identifier>ssnumber</span><span class=special>&gt;</span> <span class=special>&gt;</span>
  <span class=special>&gt;</span>
<span class=special>&gt;</span> <span class=identifier>employee_set</span><span class=special>;</span>
</pre></blockquote>

<h4>
<a name="ord_spec">Specification</a>
</h4>

<p>
Ordered index specifiers in <code>indexed_by</code> must conform to one of the 
following syntaxes:
</p>

<blockquote><pre>
<span class=special>(</span><span class=identifier>ordered_unique</span> <span class=special>|</span> <span class=identifier>ordered_non_unique</span><span class=special>)
  </span><span class=special>&lt;[</span><i>(tag)</i><span class=special>[,</span><i>(key extractor)</i><span class=special>[,</span><i>(comparison predicate)</i><span class=special>]]]&gt;</span>

<span class=special>(</span><span class=identifier>ordered_unique</span> <span class=special>|</span> <span class=identifier>ordered_non_unique</span><span class=special>)</span>
  <span class=special>&lt;[</span><i>(key extractor)</i><span class=special>[,</span><i>(comparison predicate)</i><span class=special>]]&gt;</span>
</pre></blockquote>

<p>
The first optional argument is used if <a href="#tagging">tags</a> are associated
with the index. We now proceed to briefly discuss the remaining arguments
of an ordered index specifier.
</p>

<h4>
<a name="key_extraction">Key extraction</a>
</h4>

<p>
The first template parameter (or the second, if tags are supplied)
in the specification of an ordered index provides a <i>key extraction</i> predicate.
This predicate takes a whole element (in our example, a reference to an
<code>employee</code> object) and returns the piece of information by which
the sorting is performed. In most cases, one of the following two situations arises:
<ul>
<li>The whole element serves as the key, as is the case of the first index
in <code>employee_set</code>. The predefined
<a href="key_extraction.html#identity"><code>identity</code></a> predicate
can be used here as a key extractor; <code>identity</code> returns as the key the
same object passed as argument.</li>
<li>The comparison is performed on a particular data member of the element; this
closely follows the specification of indices on a column of a table in relational
databases. Boost.MultiIndex provides
<a href="key_extraction.html#member"><code>member</code></a>, which returns
as the key a member of the element specified by a given pointer.</li>
</ul>
As an example, consider again the definition of <code>employee_set</code>. The
definition of the first index:
</p>

<blockquote><pre>
<span class=identifier>ordered_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>&gt;</span> <span class=special>&gt;</span>
</pre></blockquote>

<p>
specifies by means of <code>identity</code> that <code>element</code>
objects themselves serve as key for this index. On the other hand, in the second
index:
</p>

<blockquote><pre>
<span class=identifier>ordered_non_unique</span><span class=special>&lt;</span><span class=identifier>member</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>,</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>,&amp;</span><span class=identifier>employee</span><span class=special>::</span><span class=identifier>name</span><span class=special>&gt;</span> <span class=special>&gt;</span>
</pre></blockquote>

<p>
we use <code>member</code> to extract the <code>name</code> part of the
<code>employee</code> object. The key type of this index is then
<code>std::string</code>.
</p>

<p>
Apart from <code>identity</code> and <code>member</code>, Boost.MultiIndex provides
several other predefined key extractors and powerful ways to combine them.
Key extractors can also be defined by the user.
Consult the <a href="key_extraction.html">key extraction section</a> of
the tutorial for a more detailed exposition of this topic.
</p>

<h4><a name="comparison_predicates">Comparison predicates</a></h4>

<p>
The last part of the specification of an ordered index is the associated
<i>comparison predicate</i>, which must order the keys in a less-than fashion.
These comparison predicates are not different from those used by STL containers like
<code>std::set</code>. By default (i.e. if no comparison predicate is provided),
an index with keys of type <code>key_type</code> sorts the elements by
<code>std::less&lt;key_type></code>. Should other comparison criteria be needed,
they can be specified as an additional parameter in the index declaration:
</p>

<blockquote><pre>
<span class=comment>// define a multiply indexed set with indices by id and by name
// in reverse alphabetical order</span>
<span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span>
  <span class=identifier>employee</span><span class=special>,</span>
  <span class=identifier>indexed_by</span><span class=special>&lt;</span>
    <span class=identifier>ordered_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>&gt;</span> <span class=special>&gt;,</span> <span class=comment>// as usual</span>
    <span class=identifier>ordered_non_unique</span><span class=special>&lt;</span>
      <span class=identifier>member</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>,</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>,&amp;</span><span class=identifier>employee</span><span class=special>::</span><span class=identifier>name</span><span class=special>&gt;,</span>
      <span class=identifier>std</span><span class=special>::</span><span class=identifier>greater</span><span class=special>&lt;</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&gt;</span>  <span class=comment>// default would be std::less&lt;std::string&gt;</span>
    <span class=special>&gt;</span>
  <span class=special>&gt;</span>
<span class=special>&gt;</span> <span class=identifier>employee_set</span><span class=special>;</span>
</pre></blockquote>

<h4><a name="special_lookup">Special lookup operations</a></h4>

<p>
A given ordered index allows for lookup based on its key type, rather than the
whole element. For instance, to find Veronica Cruz in an
<code>employee_set</code> one would write:
</p>

<blockquote><pre>
<span class=identifier>employee_set</span> <span class=identifier>es</span><span class=special>;</span>
<span class=special>...</span>
<span class=keyword>typedef</span> <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>index</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>employee_set_by_name</span><span class=special>;</span>
<span class=identifier>employee_set_by_name</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;().</span><span class=identifier>find</span><span class=special>(</span><span class=string>&quot;Veronica Cruz&quot;</span><span class=special>);</span>
</pre></blockquote>

<p>As a plus, Boost.MultiIndex provides lookup operations accepting search keys
different from the <code>key_type</code> of the index, which is a specially useful
facility when <code>key_type</code> objects  are expensive to create. Ordered STL containers
fail to provide this functionality, which often leads to inelegant workarounds: consider for
instance the problem of determining the employees whose IDs fall in the range [0,100]. Given
that the key of <code>employee_set</code> index #0
is <code>employee</code> itself, on a first approach one would write the following:
</p>

<blockquote><pre>
<span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>p0</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>lower_bound</span><span class=special>(</span><span class=identifier>employee</span><span class=special>(</span><span class=number>0</span><span class=special>,</span><span class=string>&quot;&quot;</span><span class=special>));</span>
<span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>p1</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>upper_bound</span><span class=special>(</span><span class=identifier>employee</span><span class=special>(</span><span class=number>100</span><span class=special>,</span><span class=string>&quot;&quot;</span><span class=special>));</span>
</pre></blockquote>

<p>
Note however that <code>std::less&lt;employee></code> actually only depends
on the IDs of the employees, so it would be more convenient to avoid
the creation of entire <code>employee</code> objects just for the sake of
their IDs. Boost.MultiIndex allows for this: define an appropriate
comparison predicate
</p>

<blockquote><pre>
<span class=keyword>struct</span> <span class=identifier>comp_id</span>
<span class=special>{</span>
  <span class=comment>// compare an ID and an employee</span>
  <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>int</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>employee</span><span class=special>&amp;</span> <span class=identifier>e2</span><span class=special>)</span><span class=keyword>const</span><span class=special>{</span><span class=keyword>return</span> <span class=identifier>x</span><span class=special>&lt;</span><span class=identifier>e2</span><span class=special>.</span><span class=identifier>id</span><span class=special>;}</span>

  <span class=comment>// compare an employee and an ID</span>
  <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>employee</span><span class=special>&amp;</span> <span class=identifier>e1</span><span class=special>,</span><span class=keyword>int</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>{</span><span class=keyword>return</span> <span class=identifier>e1</span><span class=special>.</span><span class=identifier>id</span><span class=special>&lt;</span><span class=identifier>x</span><span class=special>;}</span>
<span class=special>};</span>
</pre></blockquote>

<p>and now write the search as</p>

<blockquote><pre>
<span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>p0</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>lower_bound</span><span class=special>(</span><span class=number>0</span><span class=special>,</span><span class=identifier>comp_id</span><span class=special>());</span>
<span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>p1</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>upper_bound</span><span class=special>(</span><span class=number>100</span><span class=special>,</span><span class=identifier>comp_id</span><span class=special>());</span>
</pre></blockquote>

<p>
Here we are not only passing IDs instead of <code>employee</code> objects:
an alternative comparison predicate is passed as well. In general, lookup operations
of ordered indices are overloaded to accept
<a href="../reference/ord_indices.html#set_operations"><i>compatible sorting
criteria</i></a>. The somewhat cumbersone definition of compatibility in this context
is given in the reference, but roughly speaking we say that a comparison predicate
<code>C1</code> is compatible with <code>C2</code> if any sequence sorted by
<code>C2</code> is also sorted with respect to <code>C1</code>.
The following shows a more interesting use of compatible predicates:
</p>

<blockquote><pre>
<span class=comment>// sorting by name's initial</span>
<span class=keyword>struct</span> <span class=identifier>comp_initial</span>
<span class=special>{</span>
  <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>char</span> <span class=identifier>ch</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>s</span><span class=special>)</span><span class=keyword>const</span><span class=special>{</span>
    <span class=keyword>if</span><span class=special>(</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>empty</span><span class=special>())</span><span class=keyword>return</span> <span class=keyword>false</span><span class=special>;</span>
    <span class=keyword>return</span> <span class=identifier>ch</span><span class=special>&lt;</span><span class=identifier>s</span><span class=special>[</span><span class=number>0</span><span class=special>];</span>
  <span class=special>}</span>

  <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>s</span><span class=special>,</span><span class=keyword>char</span> <span class=identifier>ch</span><span class=special>)</span><span class=keyword>const</span><span class=special>{</span>
    <span class=keyword>if</span><span class=special>(</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>empty</span><span class=special>())</span><span class=keyword>return</span> <span class=keyword>true</span><span class=special>;</span>
    <span class=keyword>return</span> <span class=identifier>s</span><span class=special>[</span><span class=number>0</span><span class=special>]&lt;</span><span class=identifier>ch</span><span class=special>;</span>
  <span class=special>}</span>
<span class=special>};</span>

<span class=comment>// obtain first employee whose name begins with 'J' (ordered by name)</span>
<span class=keyword>typedef</span> <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>index</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>employee_set_by_name</span><span class=special>;</span>
<span class=identifier>employee_set_by_name</span><span class=special>&amp;</span> <span class=identifier>name_index</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;();</span> 
<span class=identifier>employee_set_by_name</span><span class=special>::</span><span class=identifier>const_iterator</span> <span class=identifier>it</span><span class=special>=</span>
  <span class=identifier>name_index</span><span class=special>.</span><span class=identifier>lower_bound</span><span class=special>(</span><span class=literal>'J'</span><span class=special>,</span><span class=identifier>comp_initial</span><span class=special>());</span>
</pre></blockquote>

<h4><a name="range">Retrieval of ranges</a></h4>

<p>
Range searching, i.e. the lookup of all elements in a given interval, is a very
frequent operation for which standard <code>lower_bound</code> and
<code>upper_bound</code> can be resorted to, though in a cumbersome manner.
For instance, the following code retrieves the elements of an
<code>multi_index_container&lt;double></code> in the interval [100,200]:
</p>

<blockquote><pre>
<span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span><span class=keyword>double</span><span class=special>&gt;</span> <span class=identifier>double_set</span><span class=special>;</span>
<span class=comment>// note: default template parameters resolve to
// multi_index_container&lt;double,indexed_by&lt;unique&lt;identity&lt;double&gt; &gt; &gt; &gt;.</span>

<span class=identifier>double_set</span> <span class=identifier>s</span><span class=special>;</span>
<span class=special>...</span>
<span class=identifier>double_set</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it0</span><span class=special>=</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>lower_bound</span><span class=special>(</span><span class=number>100.0</span><span class=special>);</span>
<span class=identifier>double_set</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it1</span><span class=special>=</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>upper_bound</span><span class=special>(</span><span class=number>200.0</span><span class=special>);</span>
<span class=comment>// range [it0,it1) contains the elements in [100,200]</span>
</pre></blockquote>

<p>
Subtle changes to the code are required when strict inequalities are considered.
To retrieve the elements <i>greater</i> than 100 and <i>less</i> than 200, the
code has to be rewritten as
</p>

<blockquote><pre>
<span class=identifier>double_set</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it0</span><span class=special>=</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>upper_bound</span><span class=special>(</span><span class=number>100.0</span><span class=special>);</span>
<span class=identifier>double_set</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it1</span><span class=special>=</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>lower_bound</span><span class=special>(</span><span class=number>200.0</span><span class=special>);</span>
<span class=comment>// range [it0,it1) contains the elements in (100,200)</span>
</pre></blockquote>

<p>
To add to this complexity, the careful programmer has to take into account
that the lower and upper bounds of the interval searched be compatible: for
instance, if the lower bound is 200 and the upper bound is 100, the iterators
<code>it0</code> and <code>it1</code> produced by the code above will be in reverse
order, with possibly catastrophic results if a traversal from <code>it0</code>
to <code>it1</code> is tried. All these details make range searching a tedious
and error prone task.
</p>

<p>
The <a href="../reference/ord_indices.html#range_operations"><code>range</code></a>
member function, often in combination with
<a href="../../../../libs/lambda/index.html">Boost.Lambda</a> expressions, can
greatly help alleviate this situation:
</p>

<blockquote><pre>
<span class=keyword>using</span> <span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>lambda</span><span class=special>;</span>

<span class=keyword>typedef</span> <span class=identifier>multi_index_container</span><span class=special>&lt;</span><span class=keyword>double</span><span class=special>&gt;</span> <span class=identifier>double_set</span><span class=special>;</span>
<span class=identifier>double_set</span> <span class=identifier>s</span><span class=special>;</span>
<span class=special>...</span>
<span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>double_set</span><span class=special>::</span><span class=identifier>iterator</span><span class=special>,</span><span class=identifier>double_set</span><span class=special>::</span><span class=identifier>iterator</span><span class=special>&gt;</span> <span class=identifier>p</span><span class=special>=</span>
  <span class=identifier>s</span><span class=special>.</span><span class=identifier>range</span><span class=special>(</span><span class=number>100.0</span><span class=special>&lt;=</span><span class=identifier>_1</span><span class=special>,</span><span class=identifier>_1</span><span class=special>&lt;=</span><span class=number>200</span><span class=special>);</span> <span class=comment>// 100&lt;= x &lt;=200</span>
<span class=special>...</span>
<span class=identifier>p</span><span class=special>=</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>range</span><span class=special>(</span><span class=number>100.0</span><span class=special>&lt;</span><span class=identifier>_1</span><span class=special>,</span><span class=identifier>_1</span><span class=special>&lt;</span><span class=number>200</span><span class=special>);</span>   <span class=comment>// 100&lt;  x &lt; 200</span>
<span class=special>...</span>
<span class=identifier>p</span><span class=special>=</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>range</span><span class=special>(</span><span class=number>100.0</span><span class=special>&lt;=</span><span class=identifier>_1</span><span class=special>,</span><span class=identifier>_1</span><span class=special>&lt;</span><span class=number>200</span><span class=special>);</span>  <span class=comment>// 100&lt;= x &lt; 200</span>
</pre></blockquote>

<p>
<code>range</code> simply accepts predicates specifying the lower and upper bounds
of the interval searched. Please consult the reference for a detailed explanation
of the permissible predicates passed to <code>range</code>.</p>

<p>
One or both bounds can be omitted with the special <code>unbounded</code> marker:
</p>

<blockquote><pre>
<span class=identifier>p</span><span class=special>=</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>range</span><span class=special>(</span><span class=number>100.0</span><span class=special>&lt;=</span><span class=identifier>_1</span><span class=special>,</span><span class=identifier>unbounded</span><span class=special>);</span> <span class=comment>// 100 &lt;= x</span>
<span class=identifier>p</span><span class=special>=</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>range</span><span class=special>(</span><span class=identifier>unbounded</span><span class=special>,</span><span class=identifier>_1</span><span class=special>&lt;</span><span class=number>200.0</span><span class=special>);</span>  <span class=comment>//   x &lt;  200</span>
<span class=identifier>p</span><span class=special>=</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>range</span><span class=special>(</span><span class=identifier>unbounded</span><span class=special>,</span><span class=identifier>unbounded</span><span class=special>);</span> <span class=comment>// equiv. to std::make_pair(s.begin(),s.end())</span>
</pre></blockquote>

<h4><a name="ord_updating">Updating</a></h4>

<p>
The <a href="../reference/ord_indices.html#replace"><code>replace</code></a> member function
performs in-place replacement of a given element as the following example shows:
</p>

<blockquote><pre>
<span class=keyword>typedef</span> <span class=identifier>index</span><span class=special>&lt;</span><span class=identifier>employee_set</span><span class=special>,</span><span class=identifier>name</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>employee_set_by_name</span><span class=special>;</span>
<span class=identifier>employee_set_by_name</span><span class=special>&amp;</span> <span class=identifier>name_index</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;();</span>

<span class=identifier>employee_set_by_name</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it</span><span class=special>=</span><span class=identifier>name_index</span><span class=special>.</span><span class=identifier>find</span><span class=special>(</span><span class=string>&quot;Anna Jones&quot;</span><span class=special>);</span>
<span class=identifier>employee</span> <span class=identifier>anna</span><span class=special>=*</span><span class=identifier>it</span><span class=special>;</span>
<span class=identifier>anna</span><span class=special>.</span><span class=identifier>name</span><span class=special>=</span><span class=string>&quot;Anna Smith&quot;</span><span class=special>;</span>      <span class=comment>// she just got married to Calvin Smith</span>
<span class=identifier>name_index</span><span class=special>.</span><span class=identifier>replace</span><span class=special>(</span><span class=identifier>it</span><span class=special>,</span><span class=identifier>anna</span><span class=special>);</span> <span class=comment>// update her record</span>
</pre></blockquote>

<p>
<code>replace</code> performs this substitution in such a manner that:
<ul>
<li>The complexity is constant time if the changed element retains its original
order with respect to all indices; it is logarithmic otherwise.
<li>Iterator and reference validity are preserved.
<li>The operation is strongly exception-safe, i.e. the <code>multi_index_container</code>
remains unchanged if some exception (originated by the system or the user's data
types) is thrown.
</ul>
<code>replace</code> is a powerful operation not provided by standard STL
containers, and one that is specially handy when strong exception-safety is
required.
</p>

<p>
The observant reader might have noticed that the convenience of <code>replace</code>
comes at a cost: namely the whole element has to be copied <i>twice</i> to do
the updating (when retrieving it and inside <code>replace</code>). If elements
are expensive to copy, this may be quite a computational cost for the modification
of just a tiny part of the object. To cope with this situation, Boost.MultiIndex
provides an alternative updating mechanism called
<a href="../reference/ord_indices.html#modify"><code>modify</code></a>:
</p>

<blockquote><pre>
<span class=keyword>struct</span> <span class=identifier>change_name</span>
<span class=special>{</span>
  <span class=identifier>change_name</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>new_name</span><span class=special>):</span><span class=identifier>new_name</span><span class=special>(</span><span class=identifier>new_name</span><span class=special>){}</span>

  <span class=keyword>void</span> <span class=keyword>operator</span><span class=special>()(</span><span class=identifier>employee</span><span class=special>&amp;</span> <span class=identifier>e</span><span class=special>)</span>
  <span class=special>{</span>
    <span class=identifier>e</span><span class=special>.</span><span class=identifier>name</span><span class=special>=</span><span class=identifier>new_name</span><span class=special>;</span>
  <span class=special>}</span>

<span class=keyword>private</span><span class=special>:</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span> <span class=identifier>new_name</span><span class=special>;</span>
<span class=special>};</span>
<span class=special>...</span>
<span class=keyword>typedef</span> <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>index</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>employee_set_by_name</span><span class=special>;</span>
<span class=identifier>employee_set_by_name</span><span class=special>&amp;</span> <span class=identifier>name_index</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;();</span>

<span class=identifier>employee_set_by_name</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it</span><span class=special>=</span><span class=identifier>name_index</span><span class=special>.</span><span class=identifier>find</span><span class=special>(</span><span class=string>&quot;Anna Jones&quot;</span><span class=special>);</span>
<span class=identifier>name_index</span><span class=special>.</span><span class=identifier>modify</span><span class=special>(</span><span class=identifier>it</span><span class=special>,</span><span class=identifier>change_name</span><span class=special>(</span><span class=string>&quot;Anna Smith&quot;</span><span class=special>));</span>
</pre></blockquote>

<p><code>modify</code> accepts a functor (or pointer to function) that is
passed a reference to the element to be changed, thus eliminating the need
for spurious copies. Like <code>replace</code>, <code>modify</code> does preserve
the internal orderings of all the indices of the <code>multi_index_container</code>.
However, the semantics of <code>modify</code> is not entirely equivalent to
<code>replace</code>. Consider what happens if a collision occurs as a result
of modifying the element, i.e. the modified element clashes with another with
respect to some unique ordered index. In the case of <code>replace</code>, the
original value is kept and the method returns without altering the container, but
<code>modify</code> cannot afford such an approach, since the modifying functor
leaves no trace of the previous value of the element. Integrity constraints
thus lead to the following policy: when a collision happens in the
process of calling <code>modify</code>, the element is erased and the method returns
<code>false</code>. There is a further version of <code>modify</code> which
accepts a <i>rollback</i> functor to undo the changes in case of collision:
</p>

<blockquote><pre>
<span class=keyword>struct</span> <span class=identifier>change_id</span>
<span class=special>{</span>
  <span class=identifier>change_id</span><span class=special>(</span><span class=keyword>int</span> <span class=identifier>new_id</span><span class=special>):</span><span class=identifier>new_id</span><span class=special>(</span><span class=identifier>new_id</span><span class=special>){}</span>

  <span class=keyword>void</span> <span class=keyword>operator</span><span class=special>()(</span><span class=identifier>employee</span><span class=special>&amp;</span> <span class=identifier>e</span><span class=special>)</span>
  <span class=special>{</span>
    <span class=identifier>e</span><span class=special>.</span><span class=identifier>id</span><span class=special>=</span><span class=identifier>new_id</span><span class=special>;</span>
  <span class=special>}</span>

<span class=keyword>private</span><span class=special>:</span>
  <span class=keyword>int</span> <span class=identifier>new_id</span><span class=special>;</span>
<span class=special>};</span>
<span class=special>...</span>
<span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it</span><span class=special>=...</span>

<span class=keyword>int</span> <span class=identifier>old_id</span><span class=special>=</span><span class=identifier>it</span><span class=special>-&gt;</span><span class=identifier>id</span><span class=special>;</span> <span class=comment>// keep the original id

// try to modify the id, restore it in case of collisions</span>
<span class=identifier>es</span><span class=special>.</span><span class=identifier>modify</span><span class=special>(</span><span class=identifier>it</span><span class=special>,</span><span class=identifier>change_id</span><span class=special>(</span><span class=number>321</span><span class=special>),</span><span class=identifier>change_id</span><span class=special>(</span><span class=identifier>old_id</span><span class=special>));</span>
</pre></blockquote>

<p>In the example, <code>change_id(old_id)</code> is invoked to restore the original
conditions when the modification results in collisions with some other element.
The differences in behavior between <code>replace</code>, <code>modify</code> and
<code>modify</code> with rollback have to be considered by the programmer on a
case-by-case basis to determine the best updating mechanism.
</p>

<p align="center">
<table cellspacing="0">
  <caption><b>Behavior of the different updating mechanisms.</b></caption>
<tr>
  <th align="center">updating function</th>
  <th>If there is a collision...</th>
</tr>
<tr>
  <td align="center"><code>replace(it,x)</code></td>
  <td>replacement does not take place.</td>
</tr>
<tr class="odd_tr">
  <td align="center"><code>modify(it,mod)</code></td>
  <td>the element is erased.</td>
</tr>
<tr>
  <td align="center"><code>modify(it,mod,back)</code></td>
  <td><code>back</code> is used to restore the original conditions.
    (If <code>back</code> throws, the element is erased.)
  </td>
</tr>
</table>
</p>


<p>
Key-based versions of <code>modify</code>, named
<a href="../reference/ord_indices.html#modify_key"><code>modify_key</code></a>, are
provided as well. In this case, the modifying functors are passed a reference to
the <code>key_type</code> part of the element instead of the whole object.
</p>

<blockquote><pre>
<span class=keyword>struct</span> <span class=identifier>change_str</span>
<span class=special>{</span>
  <span class=identifier>change_str</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>new_str</span><span class=special>):</span><span class=identifier>new_str</span><span class=special>(</span><span class=identifier>new_str</span><span class=special>){}</span>

  <span class=comment>// note this is passed a string, not an employee</span>
  <span class=keyword>void</span> <span class=keyword>operator</span><span class=special>()(</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span><span class=special>&amp;</span> <span class=identifier>str</span><span class=special>)</span>
  <span class=special>{</span>
    <span class=identifier>str</span><span class=special>=</span><span class=identifier>new_str</span><span class=special>;</span>
  <span class=special>}</span>

<span class=keyword>private</span><span class=special>:</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>string</span> <span class=identifier>new_str</span><span class=special>;</span>
<span class=special>};</span>
<span class=special>...</span>
<span class=keyword>typedef</span> <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>index</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>employee_set_by_name</span><span class=special>;</span>
<span class=identifier>employee_set_by_name</span><span class=special>&amp;</span> <span class=identifier>name_index</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;();</span>

<span class=identifier>employee_set_by_name</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it</span><span class=special>=</span><span class=identifier>name_index</span><span class=special>.</span><span class=identifier>find</span><span class=special>(</span><span class=string>&quot;Anna Jones&quot;</span><span class=special>);</span>
<span class=identifier>name_index</span><span class=special>.</span><span class=identifier>modify_key</span><span class=special>(</span><span class=identifier>it</span><span class=special>,</span><span class=identifier>change_str</span><span class=special>(</span><span class=string>&quot;Anna Smith&quot;</span><span class=special>));</span>
</pre></blockquote>

<p>
Like <code>modify</code>, there are versions of <code>modify_key</code> with and
without rollback. <code>modify</code> and
<code>modify_key</code> are particularly well suited to use in conjunction to
<a href="../../../../libs/lambda/index.html">Boost.Lambda</a>
for defining the modifying functors:
</p>

<blockquote><pre>
<span class=keyword>using</span> <span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>lambda</span><span class=special>;</span>

<span class=keyword>typedef</span> <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>index</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>employee_set_by_name</span><span class=special>;</span>
<span class=identifier>employee_set_by_name</span><span class=special>&amp;</span> <span class=identifier>name_index</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;();</span>

<span class=identifier>employee_set_by_name</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it</span><span class=special>=</span><span class=identifier>name_index</span><span class=special>.</span><span class=identifier>find</span><span class=special>(</span><span class=string>&quot;Anna Jones&quot;</span><span class=special>);</span>
<span class=identifier>name_index</span><span class=special>.</span><span class=identifier>modify_key</span><span class=special>(</span><span class=identifier>it</span><span class=special>,</span><span class=identifier>_1</span><span class=special>=</span><span class=string>&quot;Anna Smith&quot;</span><span class=special>);</span>
</pre></blockquote>

<p>
<code>modify_key</code> requires that the key extractor be of
a special type called
<a href="key_extraction.html#read_write_key_extractors">read/write</a>:
this is usually, but not always, the case.
</p>

<h3>
<a name="seq_indices">Sequenced indices</a>
</h3>

<p>
Unlike ordered indices, sequenced indices do not impose a fixed order on the
elements: instead, these can be arranged in any position on the sequence, in the
same way as <code>std::list</code> permits. The interface of sequenced indices
is thus designed upon that of <code>std::list</code>; nearly every operation
provided in the standard container is replicated here, occasionally with changes
in the syntax and/or semantics to cope with the constraints imposed by
Boost.MultiIndex. An important difference, commented <a href="#iterator_access">above</a>,
is the fact that the values pointed to by sequenced index iterators are treated
as <i>constant</i>:
</p>

<blockquote><pre>
<span class=identifier>multi_index_container</span><span class=special>&lt;</span>
  <span class=keyword>int</span><span class=special>,</span>
  <span class=identifier>indexed_by</span><span class=special>&lt;</span><span class=identifier>sequenced</span><span class=special>&lt;&gt;</span> <span class=special>&gt;</span>
<span class=special>&gt;</span> <span class=identifier>s</span><span class=special>;</span>            <span class=comment>// list-like container</span>

<span class=identifier>s</span><span class=special>.</span><span class=identifier>push_front</span><span class=special>(</span><span class=number>0</span><span class=special>);</span>
<span class=special>*(</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>begin</span><span class=special>())=</span><span class=number>1</span><span class=special>;</span> <span class=comment>// ERROR: the element cannot be changed</span>
</pre></blockquote>

<p>
As with any other type of index, element modification
can nevertheless be done by means of
<a href="#seq_updating">update operations</a>.
</p>

<p>
Consider a <code>multi_index_container</code> with two or more indices, one of them
of sequenced type. If an element is inserted through another index,
then it will be automatically appended to the end of the sequenced index.
An example will help to clarify this:
</p>

<blockquote><pre>
<span class=identifier>multi_index_container</span><span class=special>&lt;</span>
  <span class=keyword>int</span><span class=special>,</span>
  <span class=identifier>indexed_by</span><span class=special>&lt;</span>
    <span class=identifier>sequenced</span><span class=special>&lt;&gt;,</span>           <span class=comment>// sequenced type</span>
    <span class=identifier>ordered_unique</span><span class=special>&lt;</span><span class=identifier>identity</span><span class=special>&lt;</span><span class=keyword>int</span><span class=special>&gt;</span> <span class=special>&gt;</span> <span class=comment>// another index</span>
  <span class=special>&gt;</span>
<span class=special>&gt;</span> <span class=identifier>s</span><span class=special>;</span>

<span class=identifier>s</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;().</span><span class=identifier>insert</span><span class=special>(</span><span class=number>1</span><span class=special>);</span> <span class=comment>// insert 1 through index #1</span>
<span class=identifier>s</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;().</span><span class=identifier>insert</span><span class=special>(</span><span class=number>0</span><span class=special>);</span> <span class=comment>// insert 0 through index #1

// list elements through sequenced index #0</span>
<span class=identifier>std</span><span class=special>::</span><span class=identifier>copy</span><span class=special>(</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>begin</span><span class=special>(),</span><span class=identifier>s</span><span class=special>.</span><span class=identifier>end</span><span class=special>(),</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>ostream_iterator</span><span class=special>&lt;</span><span class=keyword>int</span><span class=special>&gt;(</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>cout</span><span class=special>));</span>

<span class=comment>// result: 1 0</span>
</pre></blockquote>

<p>
Thus the behavior of sequenced indices when insertions are not made through
them is to preserve insertion order.
</p>

<h4><a name="seq_spec">Specification</a></h4>

<p>
Sequenced indices are specified with the <code>sequenced</code> construct:
</p>

<blockquote><pre>
<span class=identifier>sequenced</span><span class=special>&lt;[</span><i>(tag)</i><span class=special>]&gt;</span>
</pre></blockquote>

<p>
The <a href="#tagging">tag</a> parameter is optional.
</p>

<h4><a name="list_ops">List operations</a></h4>

<p>
As mentioned before, sequenced indices mimic the interface of
<code>std::list</code>, and most of the original operations therein are
provided as well. The semantics and complexity of these operations, however,
do not always coincide with those of the standard container. Differences
result mainly from the fact that insertions into a sequenced index are not
guaranteed to succeed, due to the possible banning by other indices
of the <code>multi_index_container</code>. Consult the
<a href="../reference/seq_indices.html">reference</a> for further details.
</p>

<h4><a name="seq_updating">Updating</a></h4>

<p>
Like ordered indices, sequenced indices provide
<a href="../reference/seq_indices.html#replace"><code>replace</code></a> and
<a href="../reference/seq_indices.html#modify"><code>modify</code></a>
operations, with identical functionality. There is however no analogous
<code>modify_key</code>, since sequenced indices are not key-based.
</p>

<h2><a name="projection">Projection of iterators</a></h2>

<p>
Given indices <code>i1</code> and <code>i2</code> on the same <code>multi_index_container</code>,
<a href="../reference/multi_index_container.html#projection"><code>project</code></a> can be used to
retrieve an <code>i2</code>-iterator from an <code>i1</code>-iterator, both of them
pointing to the same element of the container. This functionality allows the programmer to
move between different indices of the same <code>multi_index_container</code> when performing
elaborate operations:
</p>

<blockquote><pre>
<span class=keyword>typedef</span> <span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>index</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>employee_set_by_name</span><span class=special>;</span>
<span class=identifier>employee_set_by_name</span><span class=special>&amp;</span> <span class=identifier>name_index</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=identifier>name</span><span class=special>&gt;();</span>

<span class=comment>// list employees by ID starting from Robert Brown's ID</span>

<span class=identifier>employee_set_by_name</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it1</span><span class=special>=</span><span class=identifier>name_index</span><span class=special>.</span><span class=identifier>find</span><span class=special>(</span><span class=string>&quot;Robert Brown&quot;</span><span class=special>);</span>

<span class=comment>// obtain an iterator of index #0 from it1</span>
<span class=identifier>employee_set</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it2</span><span class=special>=</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>project</span><span class=special>&lt;</span><span class=number>0</span><span class=special>&gt;(</span><span class=identifier>it1</span><span class=special>);</span> 

<span class=identifier>std</span><span class=special>::</span><span class=identifier>copy</span><span class=special>(</span><span class=identifier>it2</span><span class=special>,</span><span class=identifier>es</span><span class=special>.</span><span class=identifier>end</span><span class=special>(),</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>ostream_iterator</span><span class=special>&lt;</span><span class=identifier>employee</span><span class=special>&gt;(</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>cout</span><span class=special>));</span>
</pre></blockquote>

<p>
A slightly more interesting example:
</p>

<blockquote><pre>
<span class=identifier>text_container</span> <span class=identifier>tc</span><span class=special>;</span>

<span class=comment>// get a view to index #1 (ordered index on the words)</span>
<span class=identifier>text_container</span><span class=special>::</span><span class=identifier>nth_index</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;::</span><span class=identifier>type</span><span class=special>&amp;</span> <span class=identifier>sorted_index</span><span class=special>=</span><span class=identifier>tc</span><span class=special>.</span><span class=identifier>get</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;();</span>

<span class=comment>// prepend &quot;older&quot; to all occurrences of &quot;sister&quot;</span>

<span class=identifier>text_container</span><span class=special>::</span><span class=identifier>nth_index</span><span class=special>&lt;</span><span class=number>1</span><span class=special>&gt;::</span><span class=identifier>type</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it1</span><span class=special>=</span>
  <span class=identifier>sorted_index</span><span class=special>.</span><span class=identifier>lower_bound</span><span class=special>(</span><span class=string>&quot;sister&quot;</span><span class=special>);</span>
  
<span class=keyword>while</span><span class=special>(</span><span class=identifier>it1</span><span class=special>!=</span><span class=identifier>sorted_index</span><span class=special>.</span><span class=identifier>end</span><span class=special>()&amp;&amp;*</span><span class=identifier>it1</span><span class=special>==</span><span class=string>&quot;sister&quot;</span><span class=special>){</span>
  <span class=comment>// convert to an iterator to the sequenced index</span>
  <span class=identifier>text_container</span><span class=special>::</span><span class=identifier>iterator</span> <span class=identifier>it2</span><span class=special>=</span><span class=identifier>tc</span><span class=special>.</span><span class=identifier>project</span><span class=special>&lt;</span><span class=number>0</span><span class=special>&gt;(</span><span class=identifier>it1</span><span class=special>);</span>

  <span class=identifier>tc</span><span class=special>.</span><span class=identifier>insert</span><span class=special>(</span><span class=identifier>it2</span><span class=special>,</span><span class=string>&quot;older&quot;</span><span class=special>);</span>
  <span class=special>++</span><span class=identifier>it1</span><span class=special>;</span>
<span class=special>}</span>
</pre></blockquote>

<p>
When provided, <code>project</code> can also be used with
<a href="#tagging">tags</a>.
</p>

<h2><a name="complexity">Complexity and exception safety</a></h2>

<p>
<code>multi_index_container</code> provides the same complexity and exception safety
guarantees as the equivalent STL containers do. Iterator and reference validity
is preserved in the face of insertions, even for replace and modify operations.
</p>

<p>
Appropriate instantiations of <code>multi_index_container</code> can in fact simulate
<code>std::set</code>, <code>std::multiset</code> and (with more limitations)
<code>std::list</code>, as shown in the
<a href="techniques.html#emulate_std_containers">techniques</a>
section. These simulations are as nearly as efficient as the original STL
containers; consult the <a href="../reference/index.html">reference</a> for further
information on complexity guarantees and the
<a href="../performance.html">performance section</a> for practical measurements of
efficiency.
</p>

<hr>

<div class="prev_link"><a href="index.html"><img src="../prev.gif" alt="tutorial" border="0"><br>
Boost.MultiIndex Tutorial
</a></div>
<div class="up_link"><a href="index.html"><img src="../up.gif" alt="Boost.MultiIndex tutorial" border="0"><br>
Boost.MultiIndex tutorial
</a></div>
<div class="next_link"><a href="indices.html"><img src="../next.gif" alt="index types" border="0"><br>
Index types
</a></div><br clear="all" style="clear: all;">

<br>

<p>Revised August 16th 2021</p>

<p>&copy; Copyright 2003-2021 Joaqu&iacute;n M L&oacute;pez Mu&ntilde;oz.
Distributed under the Boost Software 
License, Version 1.0. (See accompanying file <a href="../../../../LICENSE_1_0.txt">
LICENSE_1_0.txt</a> or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

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